{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/jermwatt/machine_learning_refined/blob/main/notes/7_Linear_multiclass_classification/7_3_Perceptron.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XnwlvA8ZcGRl"
   },
   "source": [
    "## Chapter 7: Linear multi-class classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lAY1OO26cGRn"
   },
   "source": [
    "#  7.3  Multi-Class Classification and the Perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6RSb8kVjcGRn"
   },
   "source": [
    "In this Section we discuss a natural alternative to OvA multi-class classification detailed in the previous Section.   Instead of training $C$ two class classifiers *first* and *then* fusing them into a single decision boundary (via the *fusion rule*), we can train all $C$ classifiers *simultaneously* to explicitly satisfy the fusion rule directly.  In particular here we derive the *Multi-class Perceptron* cost for achieving this feat, which can be thought of as a direct generalization of the two class perceptron described in [Section 6.4](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_4_Perceptron.html).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "7-k0JRF1cGRo"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: github-clone in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (1.2.0)\n",
      "Requirement already satisfied: requests>=2.20.0 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (2.32.3)\n",
      "Requirement already satisfied: docopt>=0.6.2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (0.6.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.4.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.10)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2.2.3)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2024.12.14)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "chapter_7_library already cloned!\n",
      "chapter_7_datasets already cloned!\n",
      "chapter_7_images already cloned!\n"
     ]
    }
   ],
   "source": [
    "# install github clone - allows for easy cloning of subdirectories\n",
    "!pip install github-clone\n",
    "from pathlib import Path \n",
    "\n",
    "# clone datasets\n",
    "if not Path('chapter_7_library').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/7_Linear_multiclass_classification/chapter_7_library\n",
    "else:\n",
    "    print('chapter_7_library already cloned!')\n",
    "\n",
    "# clone library subdirectory\n",
    "if not Path('chapter_7_datasets').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/7_Linear_multiclass_classification/chapter_7_datasets\n",
    "else:\n",
    "    print('chapter_7_datasets already cloned!')\n",
    "\n",
    "# clone datasets\n",
    "if not Path('chapter_7_images').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/7_Linear_multiclass_classification/chapter_7_images\n",
    "else:\n",
    "    print('chapter_7_images already cloned!')\n",
    "        \n",
    "\n",
    "# append path for local library, data, and image import\n",
    "import sys\n",
    "sys.path.append('./chapter_7_library') \n",
    "\n",
    "# import section helper\n",
    "import section_7_3_helpers\n",
    "\n",
    "# dataset paths\n",
    "dataset_path_1 = 'chapter_7_datasets/3class_data.csv'\n",
    "dataset_path_2 = 'chapter_7_datasets/4class_data.csv'\n",
    "\n",
    "# standard imports\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image\n",
    "import autograd.numpy as np\n",
    "\n",
    "# this is needed to compensate for matplotlib notebook's tendancy to blow up images when plotted inline\n",
    "%matplotlib inline\n",
    "from matplotlib import rcParams\n",
    "rcParams['figure.autolayout'] = True\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xTSu9_iicGRp"
   },
   "source": [
    "## The Multi-class Perceptron cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_eg_v-ATcGRp"
   },
   "source": [
    "Once again we deal with an arbitrary multi-class dataset $\\left\\{ \\left(\\mathbf{x}_{p,}\\,y_{p}\\right)\\right\\} _{p=1}^{P}$\n",
    "consisting of $C$ distinct classes of data.  The labels for these classes can be made arbitrarily, but here we will once again employ label values $y_{p}\\in\\left\\{ 0,1,...,C-1\\right\\} $.  \n",
    "\n",
    "In the previous Section on OvA multi-class classification we saw how the fusion rule rightfully defined class ownership, partitioning the input space of a dataset given its classes in a fair way.  In particular the fusion rule should *ideally when all weights are properly tuned* predict precisely the labels of our dataset as often as possible as\n",
    "\n",
    "\\begin{equation}\n",
    "y_p =   \\underset{c \\,=\\, 0,...,C-1}{\\text{argmax}} \\,\\,\\,\\mathring{\\mathbf{x}}_{p}^T \\mathbf{w}_c^{\\,}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ods9ZvTacGRq"
   },
   "source": [
    "Our aim in this Section is - instead of tuning our each classifier's weights one-by-one and then combining them in this way - to *learn all sets of weights simultaneously so as to satisfy this ideal condition as often as possible*.  Note that for now we will ignore the the beneift of *normalizing* each set of weights $\\mathbf{w}_j$, since as discussed in the prior Section this is often ignored in practice.  We will however re-introduce the concept in Section below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wKv63qDLcGRq"
   },
   "source": [
    "To get started in constructing a proper cost function by which our ideal weights can be determined upon proper minimization, first note that for the *if* the above is to hold for our $p^{th}$ point then we can likewise say that the following is true as well\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,} = \\underset{c \\,=\\, 0,...,C-1}{\\text{max}} \\,\\,\\,\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}.\n",
    "\\end{equation}\n",
    "\n",
    "Remember geometrically this simply says that the (signed) distance from the point $\\mathbf{x}_p$ to its class decision boundary is greater than its distance from every other class's. This is what we want for all of our training datapoints - to have the prediction provided by the fusion rule match our given labels, and hence the above to be true for every point $\\mathbf{x}_p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "brR_ctrLcGRq"
   },
   "source": [
    "By definition - when these weights are are tuned optimally - the right hand side of equation (2) must always be greater than or equal to the left, since the $y_p^{th}$ classifier is considered in the maximum on the right hand side.  This means that their difference - subtracting $\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}$ from both sides - gives a pointwise cost that is *always nonnegative* and minimal at zero\n",
    "\n",
    "\\begin{equation}\n",
    "g_p\\left(\\mathbf{w}_0,...,\\mathbf{w}_{C-1}\\right) = \\left(\\underset{c \\,=\\, 0,...,C-1}{\\text{max}} \\,\\,\\,\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}\\right) - \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nulJ7D6dcGRr"
   },
   "source": [
    "If our weights are set ideally this value should be zero for as many points as possible - i.e., so that the weights $\\mathbf{w}_{y_p}^{\\,}$ have been tuned correctly so that indeed the $y_p^{th}$ classifier provides the largest evaluation of $\\mathbf{x}_p$. With this in mind, we can then easily form a cost function by taking the *average* of the pointwise cost above as $\\frac{1}{P}\\sum_{p = 1}^P g_p$ or equivalently \n",
    "\n",
    "\\begin{equation}\n",
    "g\\left(\\mathbf{w}_{0}^{\\,},\\,...,\\mathbf{w}_{C-1}^{\\,}\\right) = \\frac{1}{P}\\sum_{p = 1}^P \\left[ \\left(\\underset{c \\,=\\, 0,...,C-1}{\\text{max}} \\,\\,\\,\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}\\right) - \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}\\right]\n",
    "\\end{equation}\n",
    "\n",
    "This *multi-class Perceptron* cost function is nonnegative and - when weights are tuned correctly - is as small as possible.  Thus we can stop *assuming* that we have ideal weights, and minimize this cost in order to find them.  Note here that unlike the OvA - detailed in the previous Section - here we tune all weights *simultaneously* in order to recover weights that satisfy the fusion rule in equation (1) as well as possible.  Like its two class analog (see [Section 6.4](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_4_Perceptron.html)) - the multi-class Perceptron is also *convex* regardless of the dataset employed (also see this Chapter's exercises for further details).  It also has a *trivial solution at zero*, that is when $\\mathbf{w}_c = \\mathbf{0}$ for all $c$ the cost is minimal which is to be avoided (which is often achievable by initializing any local optimization scheme used to minimize it away from the origin). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5cWlaMEucGRr"
   },
   "source": [
    "##  Nomenclature and alternative formulations of the multi-class Perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WuYAqSF1cGRr"
   },
   "source": [
    "We call this the *multi-class Perceptron cost* not only because we have derived it by studying the problem of multi-class classification 'from above' as we did in [Section 6.4](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_4_Perceptron.html), but also due to the fact that it can be easily shown to be a direct generalization of the two class version introduced in Section 6.4.1.  One easy way to see this is rewrite it - in order to make its appearence more akin to its two class analog - by combining the two terms in each summand using the following simple property of the $\\text{max}$ function\n",
    "\n",
    "\\begin{equation}\n",
    "{\\text{max}} \\left(s_0,\\,s_1,...,s_{C-1}\\right) - z = {\\text{max}} \\left(s_0 - z,\\,s_1 - z,...,s_{C-1} - z\\right)\n",
    "\\end{equation}\n",
    "\n",
    "where $s_0,\\,s_1,...,s_{C-1}$ and $z$ are scalar values.  Using this we can combine both terms in the $p^{th}$ summand andre-write the multi-class Perceptron in equation (4) cost function as follows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qmw4-wVKcGRr"
   },
   "source": [
    "\\begin{equation}\n",
    "g\\left(\\mathbf{w}_{0}^{\\,},\\,...,\\mathbf{w}_{C-1}^{\\,}\\right) = \\frac{1}{P}\\sum_{p = 1}^P \\underset{ \\underset{c \\neq y_p }{ c \\,=\\, 0,...,C-1}  }{\\text{max}} \\left(0,\\mathring{\\mathbf{x}}_{p}^T\\left( \\overset{\\,}{\\mathbf{w}}_c^{\\,} - \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}\\right)\\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZR77JA4QcGRs"
   },
   "source": [
    "Here we can see that the corresponding pointwise cost $g_p\\left(\\mathbf{w}_0,...,\\mathbf{w}_{C-1}\\right) = \\underset{ \\underset{c \\neq y_p }{ c \\,=\\, 0,...,C-1}  }{\\text{max}} \\left(0,\\mathring{\\mathbf{x}}_{p}^T\\left( \\overset{\\,}{\\mathbf{w}}_c^{\\,} - \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}\\right)\\right)$ now mirrors its the two class analog detailed in 6.4.1 more closely.  In this form it is straightforward to then show that when $C = 2$ the multi-class Perceptron reduces to the two class version."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XCvosCyXcGRs"
   },
   "source": [
    "##  Regularization and the multi-class Perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "oC11n6PhcGRs"
   },
   "source": [
    "Note how in minimizing this cost we should - at least formally - subject it to the constraints that all feature-touching portions / normal vectors have unit length.  To express this we will employ our bias / feature-touching weight notation allowing us to decompose each weight vector $\\mathbf{w}_c$ into two components\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{(bias):}\\,\\, b_c = w_{0,c} \\,\\,\\,\\,\\,\\,\\,\\, \\text{(feature-touching weights):} \\,\\,\\,\\,\\,\\, \\boldsymbol{\\omega}_j = \n",
    "\\begin{bmatrix}\n",
    "w_{1,c} \\\\\n",
    "w_{2,c} \\\\ \n",
    "\\vdots \\\\\n",
    "w_{N,c}\n",
    "\\end{bmatrix}.\n",
    "\\end{equation}\n",
    "\n",
    "In this notation each linear combination can be written as $\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,} =  b_{c}^{\\,} + \\mathbf{x}_{p}^T\\boldsymbol{\\omega}_{c}^{\\,}$.\n",
    "\n",
    "\n",
    "The formal desire for the feature-touching weights from all $C$ classifiers to have unit length translates to $\\left \\Vert \\boldsymbol{\\omega}_{c}^{\\,} \\right \\Vert_2^2 = 1$ for all $c$. As detailed in the previous Section, formally speaking we need these normal vectors to be unit length if we are to fairly compare the distance of each input $\\mathbf{x}_p$ to our two-class decision boundaries.    Doing this, a proper *constrained optimization* problem involving our multi-class Perceptron takes the form\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "\\underset{b_{0}^{\\,},\\,\\boldsymbol{\\omega}_{0}^{\\,},\\,...,\\,b_{C-1}^{\\,},\\,\\boldsymbol{\\omega}_{C-1}^{\\,}}{\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\mbox{minimize}\\,\\,\\,} & \\,\\,\\,\\,  \\frac{1}{P}\\sum_{p = 1}^P \\left[\\left(\\underset{c \\,=\\, 0,...,C-1}{\\text{max}} \\,\\,\\,b_{c}^{\\,} + \\mathbf{x}_{p}^T\\boldsymbol{\\omega}_{c}^{\\,}\\right) - \\left(b_{y_p}^{\\,} + \\mathbf{x}_{p}^T\\boldsymbol{\\omega}_{y_p}^{\\,}\\right)\\right]\\\\\n",
    "\\mbox{subject to}\\,\\,\\, & \\,\\,\\,\\,\\, \\left \\Vert \\boldsymbol{\\omega}_{c}^{\\,} \\right \\Vert_2^2  = 1, \\,\\,\\,\\,\\,\\, c \\,=\\, 0,...,C-1\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "This is a proper cost function for *determining* proper weights for our $C$ classifiers: it is always nonnegative, we want to find weights so that its value is small, and it is precisely zero when all training points are classified correctly.  We can solve such problems directly in a variety of ways - e.g., by using projected gradient descent - but it is more commonplace to see this problem approximately solved by *relaxing the constraints* (as we have seen done many times before, e.g., in Sections [6.4.3](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_4_Perceptron.html) and [6.5.3](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_5_SVMs.html))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3QKdXbu6cGRs"
   },
   "source": [
    "This means we can phrase this constrained problem in an unconstrained *regularized* form by relaxing the constraints but penalizing their magnitude. Because we have $C$ constraints we could in theory provide a distinct penalty (or regularization parameter) $\\lambda_j$ for each constraint. However for simplicity one can choose a single regularization parameter $\\lambda \\geq 0$ that is used to penalize the magnitude of all normal vectors simultaneously. This way we need only provide one regularization value instead of $C$ distinct regularization parameters, giving the regularized form of the above problem giving a regularized multi-class Perceptron cost function\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{1}{P}\\sum_{p = 1}^P \\left[\\left(\\underset{c \\,=\\, 0,...,C-1}{\\text{max}} \\,\\,\\,b_{c}^{\\,} + \\mathbf{x}_{p}^T\\boldsymbol{\\omega}_{c}^{\\,}\\right) - \\left(b_{y_p}^{\\,} + \\mathbf{x}_{p}^T\\boldsymbol{\\omega}_{y_p}^{\\,}\\right)\\right]+ \\lambda \\sum_{c = 0}^{C-1} \\left \\Vert \\boldsymbol{\\omega}_{c}^{\\,} \\right \\Vert_2^2 \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8ABrzCsJcGRt"
   },
   "source": [
    "that must be minimized properly. This regularized form does not quite match the original constrained formulation as regularizing all normal vectors together will not necessarily guarantee that $\\left \\Vert \\boldsymbol{\\omega}_{c}^{\\,} \\right \\Vert_2^2 = 1$ for all $c$.  However it will generally force the length of all normal vectors to behave well, e.g., disallowing one normal vector to grow arbitrarily large while one shrinks to almost nothing. As we see many times in machine learning, it is commonplace to make such compromises to get something that is 'close enough' to the original as long as it does work well in practice. This is indeed the case here with $\\lambda$ typically set to a small value (e.g., $10^{-3}$ and smaller)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vxRaGrrscGRt"
   },
   "source": [
    "##  Implementing and minimizing a modular multi-class Perceptron in `Python`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "81JQhLkUcGRt"
   },
   "source": [
    "To take advantage of the `numpy` libraries fast array operations we use the notation first initroduced in [Section 5.6.3](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_6_Multi.html), and repeated in the previous Section, we stack the trained weights from our $C$ classifiers together into a single $\\left(N + 1\\right) \\times C$ array of the form\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{W}=\\begin{bmatrix} \n",
    "w_{0,0}  &  w_{0,1}  &  w_{0,2}  & \\cdots   &  w_{0,C-1}  \\\\\n",
    "w_{1,0}  &  w_{1,1}  &  w_{1,2}  & \\cdots  &   w_{1,C-1}  \\\\\n",
    "w_{2,0}  &  w_{2,1}  &  w_{2,2}  & \\cdots  &  w_{2,C-1}  \\\\\n",
    "\\,\\,\\, {\\vdots}_{\\,\\,\\,}  & {\\vdots}_{\\,\\,\\,}  &  {\\vdots}_{\\,\\,\\,}  &  \\cdots   &    {\\vdots}_{\\,\\,\\,}    \\\\\n",
    "w_{N,0}  &  w_{N,1} & w_{N,2}  &  \\cdots  &  w_{N,C-1}  \\\\\n",
    "\\end{bmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ma-pPq5hcGRt"
   },
   "source": [
    "Here the bias and normal vector of the $c^{th}$ classifier have been stacked on top of one another and make up the $c^{th}$ column of the array.  Now lets extend our `model` notation to also denote the evaluation of our $C$ individual linear models as\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{matrix} \n",
    "\\text{model}\\left(\\mathbf{x},\\mathbf{W}\\right) = \\mathring{\\mathbf{x}}_{\\,}^T\\mathbf{W} \\end{matrix}  = \\begin{bmatrix}\n",
    "\\mathring{\\mathbf{x}}_{\\,}^T  \\overset{\\,}{\\mathbf{w}}_{0}^{\\,}   &\n",
    "\\mathring{\\mathbf{x}}_{\\,}^T  \\overset{\\,}{\\mathbf{w}}_{1}^{\\,}   &\n",
    "\\cdots \\, &\n",
    "\\mathring{\\mathbf{x}}_{\\,}^T  \\overset{\\,}{\\mathbf{w}}_{C-1}^{\\,}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RJv7-fjXcGRu"
   },
   "source": [
    "Note: not only is this the *same* linear model used in multi-output regression (as detailed in [Section 5.6](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_6_Multi.html)), but the above is a $1\\times C$ array of our linear models that can be evaluated at any $\\mathbf{W}$.  We can now use precisely the same `model` implementation we have seen in Section 5.6.3, which we repeat below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "0W_wgDNTcGRu"
   },
   "outputs": [],
   "source": [
    "# compute C linear combinations of input point, one per classifier\n",
    "def model(x,w):\n",
    "    a = w[0] + np.dot(x.T,w[1:])\n",
    "    return a.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YddSF2xScGRu"
   },
   "source": [
    "With this `model` notation we can more conveniently implement essentially any formula derived from the fusion rule like e.g., the multi-class Perceptron.  For example, we can write the fusion rule itself equivalently as \n",
    "\n",
    "\\begin{equation}\n",
    "y = \\underset{c \\,=\\, 0,...,C-1} {\\text{max}}\\,\\text{model}\\left(\\mathbf{x},\\mathbf{W}\\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4PEj0kzYcGRu"
   },
   "source": [
    "Likewise we can write the $p^{th}$ summand of the multi-class Perceptron compactly as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rw1WrG4jcGRu"
   },
   "source": [
    "\n",
    "\\begin{equation}\n",
    "\\left(\\underset{c \\,=\\, 0,...,C-1}{\\text{max}} \\,\\,\\,\\mathring{\\mathbf{x}}_{p}^T \\mathbf{w}_c^{\\,}\\right) - \\mathring{\\mathbf{x}}_{p}^T \\mathbf{w}_{y_p}^{\\,}. = \\left(\\underset{c \\,=\\, 0,...,C-1} {\\text{max}}\\,\\text{model}\\left(\\mathbf{x}_p,\\mathbf{W}\\right)\\right) - \\text{model}\\left(\\mathbf{x}_p,\\mathbf{W}\\right)_{y_p}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Qoa3VrHGcGRu"
   },
   "source": [
    "With this in mind we can then easily implement a multi-class Perceptron in `Python` looping over each point explicitly, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "enc8f_JAcGRv"
   },
   "outputs": [],
   "source": [
    "# multi-class perceptron regularized by the summed length of all normal vectors\n",
    "lam = 10**-5  # our regularization paramter \n",
    "def multiclass_perceptron(w):        \n",
    "    # pre-compute predictions on all points\n",
    "    all_evals = model(x,w)\n",
    "\n",
    "    # compute counting cost\n",
    "    cost = 0\n",
    "    for p in range(len(y)):\n",
    "        # pluck out current true label\n",
    "        y_p = y[p] \n",
    "\n",
    "        # update cost summand\n",
    "        cost +=  np.max(all_evals[p,:]) - all_evals[p,int(y_p)]\n",
    "        \n",
    "    # return cost with regularizer added\n",
    "    cost += lam*np.linalg.norm(w[1:,:],'fro')**2\n",
    "    return cost/float(len(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AjUwe3JncGRv"
   },
   "source": [
    "``Python`` code often runs much faster when ``for`` loops - or equivalently ``list comprehensions`` - are written equivalently using matrix-vector ``numpy`` operations (this has been a constant theme in our implementations since linear regression in [Section 5.2](https://jermwatt.github.io/machine_learning_refined/notes/5_Linear_regression/5_2_Least.html)).  This often leads to more compact ``Python`` code as well, since ``for`` loop operations are often more compactly written (even mathematically) as a matrix-vector operations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3YJ9K-0VcGRv"
   },
   "source": [
    "Below we show an example of writing the ``multiclass_perceptron`` cost function more compactly than shown previously using ``numpy`` operations instead of the explicit ``for`` loop over the data points.  Both this and the previous implementation compute the same final result for a given set of input weights, but here the computation will be considerably (orders of magnitude) faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "rjj8j0PocGRv"
   },
   "outputs": [],
   "source": [
    "lam = 10**-5  # our regularization paramter \n",
    "def multiclass_perceptron(w):        \n",
    "    # pre-compute predictions on all points\n",
    "    all_evals = model(x,w)\n",
    "    \n",
    "    # compute maximum across data points\n",
    "    a = np.max(all_evals,axis = 0)    \n",
    "\n",
    "    # compute cost in compact form using numpy broadcasting\n",
    "    b = all_evals[y.astype(int).flatten(),np.arange(np.size(y))]\n",
    "    cost = np.sum(a - b)\n",
    "    \n",
    "    # add regularizer\n",
    "    cost = cost + lam*np.linalg.norm(w[1:,:],'fro')**2\n",
    "    \n",
    "    # return average\n",
    "    return cost/float(np.size(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qqe_xLZhcGRv"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 1: </span> multi-class perceptron"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EjA91YAqcGRv"
   },
   "source": [
    "In this example we minimize the regularized multi-class classifier defined above over a toy dataset with $C=3$ classes used in deriving OvA in the previous Section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "M2WQdjtWcGRw",
    "outputId": "fb5959a4-15bf-43cc-f45d-ef15d24e8668"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1700x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load in dataset\n",
    "data = np.loadtxt(dataset_path_1,delimiter = ',')\n",
    "\n",
    "# get input/output pairs\n",
    "x = data[:-1,:]\n",
    "y = data[-1:,:] \n",
    "\n",
    "# create an instance of the ova demo\n",
    "demo = section_7_3_helpers.MulticlassVisualizer(data)\n",
    "\n",
    "# visualize dataset\n",
    "demo.show_dataset()\n",
    "\n",
    "# run gradient descent to minimize cost\n",
    "g = multiclass_perceptron; w = 0.1*np.random.randn(3,3); max_its = 2000; alpha_choice = 10**(-1);\n",
    "weight_history = demo.gradient_descent(g,w,alpha=alpha_choice,max_its=max_its)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WVt-bIpMcGRx"
   },
   "source": [
    "With our multi-class classifier trained by gradient descent we now show how it classifies the entire input space. In the left panel we plot each individual two-class classifier. In the middle panel we show the fused multi-class decision boundary formed by combining these individual classifiers via the fusion rule. In the right panel we plot the cost function value over $200$ iterations of gradient descent.\n",
    "\n",
    "Note in the left panel that because we did not train each individual classifier in an OvA sense - but trained them together all at once - each individual learned two-class classifier performs quite poorly.  This is fine as our cost function aimed at minimizing all errors of every class simultaneously and not two at a time as with OvA - so we need not expect each individual classifier to cut the space well. However since they were learned together their combination - using the fusion rule - provides a multi-class decision boundary with zero errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "oCqFR2HAcGRx",
    "outputId": "82ae9500-e2ec-4cac-b131-ffe8cebbd5f2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot classification of space, individual learned classifiers (left panel) and joint boundary (middle panel), and cost-function panel in the right panel\n",
    "demo.show_complete_coloring(weight_history, cost = multiclass_perceptron)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mSt_0WBWcGRx"
   },
   "source": [
    "##  The Multi-class Softmax / Cross Entropy cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JL50pB69cGRx"
   },
   "source": [
    "As we saw previously with the case of the two class perceptron in [Section 6.4](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_4_Perceptron.html), we are often willing to sacrifice a small amount of modeling precision - forming a closely matching smoother cost function to the one we already have - in order to make optimization easier or expand the optimization tools we can bring to bear.  As was the case with the two class perceptron, here too we can *smooth* the multi-class Perceptron cost employing the *softmax* function.  Recall from our discussion of the two class perceptron in Section 6.4.2 that the *softmax function*\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{soft}\\left(s_0,s_1,...,s_{C-1}\\right) = \\text{log}\\left(e^{s_0} + e^{s_1} + \\cdots + e^{s_{C-1}} \\right)\n",
    "\\end{equation}\n",
    "\n",
    "is a close and smooth approximation to the maximum of $C$ scalar numbers $s_{0},...,s_{C-1}$, i.e.,\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{soft}\\left(s_0,s_1,...,s_{C-1}\\right) \\approx \\text{max}\\left(s_0,s_1,...,s_{C-1}\\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UUOE8cy8cGRy"
   },
   "source": [
    "Replacing the $\\text{max}$ function in each summand of the multi-class Perceptron *as written in equation (4)* above with its $\\text{softmax}$ approximation gives have the following cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QxRqoJPZcGRy"
   },
   "source": [
    "\\begin{equation}\n",
    "g\\left(\\mathbf{w}_{0}^{\\,},\\,...,\\mathbf{w}_{C-1}^{\\,}\\right) = \\frac{1}{P}\\sum_{p = 1}^P \\left[\\text{log}\\left( \\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}}  \\right) - \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}\\right].\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "n7nJIxk-cGRy"
   },
   "source": [
    "This is referred to as the *multi-class Softmax* cost function is convex but - unlike the Multiclass Perceptron - it has infinitely many smooth derivatives, hence we can use second order methods (in addition to gradient descent) in order to properly minimize it.  Notice that it also no longer has a trivial solution at zero, i.e., when $\\mathbf{w}_j = \\mathbf{0}$ for all $j$ (just as its two class analog removed this deficiency - see Section 6.4.3)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZsmSyGLbcGRy"
   },
   "source": [
    "## Nomenclature and alternative formulations of the multi-class Softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "THWQEBd_cGRy"
   },
   "source": [
    "This cost function goes by *many* names in practice including: the *multi-class Softmax*, *Multiclass Cross Entropy*, *Softplus*, and *Multiclass Logistic* cost to name a few.  We however will use two fundamental names to refer to it in general.  The first is *Multiclass Softmax*, which we use both because it is a softmax-smoothed version of the Multiclass Perceptron and because it is the natural generalization of the two class version seen in e.g., [Section 6.4.3](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_4_Perceptron.html).  To see this more easily let us smooth the formulation of the Multiclass Perceptron given in equation (6), replacing the $\\text{max}$ with the $\\text{softmax}$ approximation, giving an equivalent but different formulation than the one above\n",
    "\n",
    "\\begin{equation}\n",
    "g\\left(\\mathbf{w}_{0}^{\\,},\\,...,\\mathbf{w}_{C-1}^{\\,}\\right) = \\frac{1}{P}\\sum_{p = 1}^P  \\text{log}\\left(1 + \\sum_{\\underset{j \\neq y_p}{c = 0}}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\left(\\overset{\\,}{\\mathbf{w}}_c^{\\,} - \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}\\right)}  \\right).\n",
    "\\end{equation}\n",
    "\n",
    "Visually this appears more similar to the two class Softmax cost, and indeed does reduce to it when $C = 2$ (and $y_p \\in \\left\\{-1,+1\\right\\}$ are chosen)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "otfsORlUcGRy"
   },
   "source": [
    "We will also refer to this function as the *multi-class Cross Entropy* cost because it is - likewise - a natrual generalization of the two class version seen in [Section 6.2](https://jermwatt.github.io/machine_learning_refined/notes/6_Linear_twoclass_classification/6_2_Cross_entropy.html).  To see that this indeed the case we can again re-express the Softmax cost in equation (16) in an equivalent but different way.  To do this note that we take its $p^{th}$ summand and rewrite it using the fact that $\\text{log}\\left(e^{s}\\right) = s$ as\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{log}\\left( \\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}}  \\right) - \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,} = \\text{log}\\left( \\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}}  \\right) - \\text{log}\\,e^{\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NGqrr0-9cGRz"
   },
   "source": [
    "Now we can use the $\\text{log}$ property that \n",
    "\n",
    "\\begin{equation}\n",
    " \\text{log}\\left(s\\right) - \\text{log}\\left(t\\right) = \\text{log}\\left(\\frac{s}{t}\\right) \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3G-9TfVocGRz"
   },
   "source": [
    "to rewrite the above as \n",
    "\n",
    "\\begin{equation}\n",
    "\\text{log}\\left( \\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}}  \\right) - \\text{log}\\,e^{\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}} = \\text{log}\\left( \\frac{\\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}}}  {e^{\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}}}    \\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TQIrXg-TcGRz"
   },
   "source": [
    "Finally because by the $\\text{log}$ property that\n",
    "\n",
    "\\begin{equation}\n",
    "\\text{log}\\left(s\\right) = -\\text{log}\\left(\\frac{1}{s}\\right)\n",
    "\\end{equation}\n",
    "\n",
    "this can be rewritten equivalently as \n",
    "\n",
    "\\begin{equation}\n",
    "\\text{log}\\left( \\frac{ \\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}}}  {e^{\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}}}    \\right) = -\\text{log}\\left( \\frac{e^{\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}}}  {\\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}} }    \\right) \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pbXwJXs5cGRz"
   },
   "source": [
    "So in sum, we can rewrite \n",
    "\n",
    "\\begin{equation}\n",
    "g\\left(\\mathbf{w}_{0}^{\\,},\\,...,\\mathbf{w}_{C-1}^{\\,}\\right) = -\\frac{1}{P}\\sum_{p = 1}^P  \\text{log}\\left( \\frac{e^{\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}}}  {\\sum_{c = 0}^{C-1}  e^{ \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}} }    \\right) .\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RSkXjYnFcGRz"
   },
   "source": [
    "Visually this appears more similar to the two class Cross Entropy cost [1], and indeed does reduce to it in quite a straightforward manner when $C = 2$ (and $y_p \\in \\left\\{0,1\\right\\}$ are chosen)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d9Wd-FTAcGRz"
   },
   "source": [
    "##  Regularization and the multi-class Softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dqM3grQfcGRz"
   },
   "source": [
    "As with the multi-class Percpetron, it is common to *regularize* the Multiclass Softmax via its feature touching weights as \n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{1}{P}\\sum_{p = 1}^P \\left[\\text{log}\\left( \\sum_{c = 0}^{C-1}  e^{ b_{c}^{\\,} + \\mathbf{x}_{p}^T\\boldsymbol{\\omega}_{c}^{\\,} }  \\right) - \\left(b_{y_p}^{\\,} + \\mathbf{x}_{p}^T\\boldsymbol{\\omega}_{y_p}^{\\,}\\right)\\right] + \\lambda \\sum_{c = 0}^{C-1} \\left \\Vert \\boldsymbol{\\omega}_{c}^{\\,} \\right \\Vert_2^2 \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eMsoEB2rcGR0"
   },
   "source": [
    "where $\\lambda \\geq 0$ is typically set to a small value like e.g., $10^{-3}$.  In addition to this being more formally appropriate - given that our cost funtions originate with the fusion rule established in the previous Section - this can also be interpreted as a way of preventing local optimization methods like Newton's method (which take large steps) from diverging when dealing with perfectly seperable data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7nCxofMtcGR0"
   },
   "source": [
    "##  Implementing and minimizing a modular multi-class softmax in `Python`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7D12PWCmcGR0"
   },
   "source": [
    "We can implement the multi-class Softmax cost very similar to how the Multiclass Perceptron was implemented above.  That is, using the compact model notation introduced there"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dizzxJ1ocGR0"
   },
   "source": [
    "\\begin{equation}\n",
    "\\begin{matrix} \n",
    "\\text{model}\\left(\\mathbf{x},\\mathbf{W}\\right) = \\mathring{\\mathbf{x}}_{\\,}^T\\mathbf{W} \\end{matrix}  = \\begin{bmatrix}\n",
    "\\mathring{\\mathbf{x}}_{\\,}^T  \\overset{\\,}{\\mathbf{w}}_{0}^{\\,}   &\n",
    "\\mathring{\\mathbf{x}}_{\\,}^T  \\overset{\\,}{\\mathbf{w}}_{1}^{\\,}   &\n",
    "\\cdots \\, &\n",
    "\\mathring{\\mathbf{x}}_{\\,}^T  \\overset{\\,}{\\mathbf{w}}_{C-1}^{\\,}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dc98orIbcGR0"
   },
   "source": [
    "we can likewise implement the evaluation of all $C$ classifiers simply as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "JOrYPw65cGR0"
   },
   "outputs": [],
   "source": [
    "# compute C linear combinations of input point, one per classifier\n",
    "def model(x,w):\n",
    "    a = w[0] + np.dot(x.T,w[1:])\n",
    "    return a.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dEyj9JEDcGR0"
   },
   "source": [
    "Likewise we can write the $p^{th}$ summand of the multi-class Softmax (as written in equation (16)) compactly as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zIoz7GzAcGR0"
   },
   "source": [
    "\n",
    "\\begin{equation}\n",
    "\\left(\\underset{c \\,=\\, 0,...,C-1}{\\text{softmax}} \\,\\,\\,\\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_c^{\\,}\\right) - \\mathring{\\mathbf{x}}_{p}^T \\overset{\\,}{\\mathbf{w}}_{y_p}^{\\,}. = \\left(\\underset{c \\,=\\, 0,...,C-1} {\\text{softmax}}\\,\\text{model}\\left(\\mathbf{x}_p,\\mathbf{W}\\right)\\right) - \\text{model}\\left(\\mathbf{x}_p,\\mathbf{W}\\right)_{y_p}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sLQMILhscGR1"
   },
   "source": [
    "With this more compact way of expressing the multi-class softmax - and with the module `model` having already been written above - we can quickly implement a `Python` efficient implementation of the Multi-class Softmax cost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "WEiXxvHocGR1"
   },
   "outputs": [],
   "source": [
    "# multiclass softmaax regularized by the summed length of all normal vectors\n",
    "lam = 10**(-5)  # our regularization paramter \n",
    "def multiclass_softmax(w):        \n",
    "    # pre-compute predictions on all points\n",
    "    all_evals = model(x,w)\n",
    "    \n",
    "    # compute softmax across data points\n",
    "    a = np.log(np.sum(np.exp(all_evals),axis = 0)) \n",
    "    \n",
    "    # compute cost in compact form using numpy broadcasting\n",
    "    b = all_evals[y.astype(int).flatten(),np.arange(np.size(y))]\n",
    "    cost = np.sum(a - b)\n",
    "    \n",
    "    # add regularizer\n",
    "    cost = cost + lam*np.linalg.norm(w[1:,:],'fro')**2\n",
    "    \n",
    "    # return average\n",
    "    return cost/float(np.size(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "id": "h9SOnLECcGR1"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 2: </span> Multi-class Softmax on a toy dataset with $C=3$ classes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NP6gg5YXcGR1"
   },
   "source": [
    "In this example we run the multi-class softmax classifier on the same dataset used in the previous example, first using unnormalized gradient descent and then Newton's method.  In the next Python cell we implement a version of the multi-class softmax cost function complete with regularizer. The weights are formatted precisely as in our implementation of the multi-class perceptron, discussed in Example 1.  We then minimize the softmax cost function using gradient descent - for $200$ iterations using a fixed steplength value $\\alpha = 10^{-2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AnsNM9aAcGR1"
   },
   "source": [
    "Below we plot the final classification over the entire space in the left and middle panels while the cost function plot from our run of gradient descent is plotted in the right panel. In the left panel are shown the final learned two-class classifiers individually, in the middle the multi-class boundary created using these two-class boundaries and the fusion rule. As with the multi-class perceptron, since the multi-class softmax cost focuses on optimizing the parameters of all $C$ two-class classifiers simultaneously to get the best multi-class fit, each one of the two-class decision boundaries need not perfectly distinguish its class from the rest of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "RCVuG4ulcGR1",
    "outputId": "db4b66a0-c184-4631-bd10-ec07b5f49d84"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load in dataset\n",
    "data = np.loadtxt(dataset_path_1,delimiter = ',')\n",
    "\n",
    "# create instance of multiclass visualizer\n",
    "demo = section_7_3_helpers.MulticlassVisualizer(data)\n",
    "\n",
    "# run gradient descent to minimize cost\n",
    "g = multiclass_softmax; w = 0.1*np.random.randn(3,3); max_its = 200; alpha_choice = 1;\n",
    "weight_history = demo.gradient_descent(g,w,alpha=alpha_choice,max_its=max_its)\n",
    "\n",
    "# plot classification of space, individual learned classifiers (left panel) and joint boundary (middle panel), and cost-function panel in the right panel\n",
    "demo.show_complete_coloring(weight_history, cost = multiclass_softmax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aDkx5H94cGR2"
   },
   "source": [
    "Optimizing using Newton's method takes just a few steps: in the next cell we re-run the above experiment only using 5 Newton steps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KY6y7hwWcGR2"
   },
   "source": [
    "Below we then print out the same panels as previously, only displaying the results of Newton's method.  Using just a few steps we reach a far lower point on the Multi-class Softmax function - as can be seen by comparing the right panel below with the one shown previously with gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "C-hBADdlcGR2",
    "outputId": "61b44cfc-4a07-40b2-ecf2-813fe0f6d89a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# run newtons method to minimize cost\n",
    "g = multiclass_softmax; w = 0.1*np.random.randn(3,3); max_its = 5; \n",
    "weight_history = demo.newtons_method(g,w,max_its=max_its)\n",
    "\n",
    "# plot classification of space, individual learned classifiers (left panel) and joint boundary (middle panel), and cost-function panel in the right panel\n",
    "demo.show_complete_coloring(weight_history, cost = multiclass_softmax)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WoX5bT_2cGR2"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 3: </span> Multi-class Softmax on a toy dataset with $C = 4$ classes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Zz_beisycGR2"
   },
   "source": [
    "Here we quickly apply Newton's method to fit the Multi-sclass Softmax cost to our toy dataset with $C=4$ classes.  Here points colred red, blue, green, and kahki have label values $y_p = 0$, $1$, $2$, and $3$ respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "ERjd49YxcGR2",
    "outputId": "e3cf1e43-aa3d-434c-c232-04f1c2262fe4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1700x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# load in dataset\n",
    "data = np.loadtxt(dataset_path_2,delimiter = ',')\n",
    "\n",
    "# get input/output pairs\n",
    "x = data[:-1,:]\n",
    "y = data[-1:,:] \n",
    "\n",
    "# create instance of multiclass visualizer\n",
    "demo = section_7_3_helpers.MulticlassVisualizer(data)\n",
    "\n",
    "# visualize dataset\n",
    "demo.show_dataset()\n",
    "\n",
    "# run gradient descent to minimize cost\n",
    "g = multiclass_softmax; w = 0.1*np.random.randn(3,4); max_its = 5; \n",
    "weight_history = demo.newtons_method(g,w,max_its=max_its)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ozYs3QsUcGR3"
   },
   "source": [
    "Finally, we plot our results, as in the previous Example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "kh095CbpcGR3",
    "outputId": "40d05309-1224-4f03-be82-6982bf45fd0b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot classification of space, individual learned classifiers (left panel) and joint boundary (middle panel), and cost-function panel in the right panel\n",
    "demo.show_complete_coloring(weight_history, cost = multiclass_softmax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "P49Pu32fcGR3"
   },
   "source": [
    "##  End notes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "plm8Stv7cGR3"
   },
   "source": [
    "[1]  Care must be taken when implementing any cost function - or mathematical expression in general - involving the exponential function $e^{\\left(\\cdot\\right)}$ in Python. By nature the exponential function grows large very rapidly causing undesired 'overflow' issues even with moderate-sized exponents, e.g., $e^{1000}$. Large numbers like this cannot be stored explicitly on the computer and so are represented symbolically as $\\infty$. Additionally, the division of two such large numbers - which is a potentiality when evaluating the summands of the multi-class cost in equation (6) - is computed and stored as a NaN (not a number) causing severe numerical stability issues.\n",
    "\n",
    "One way we can guard against this issue is by normalizing the data - to fall within a relatively small range - and regularizing the the feature-touching weights, to punish/prevent large weight values. While a workable solution, in practice we can still run into overflow issues immediately after initialization especially when input is high-dimensional. It is therefore good practice to implement one's own version of the exponential function by capping the maximum value it can take, as shown below where $G$ is set to a relatively large value that does not send $e^G$ to $\\infty$.  "
   ]
  }
 ],
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